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StarCoffee is the only place that sells coffee at HKBU (assume there is no other place that HKBU students can go to)

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StarCoffee is the only place that sells coffee at HKBU (assume there is no other place that HKBU students can go to). The student's total demand for coffee is Qs(P) = 6 - P. Lily can produce one cup of coffee at a constant marginal cost of $2. Now suppose Faculty Club is closed due to construction. Professors also go to Lily Coffee. The professor's total demand for coffee is Qf(P) = 8-1/3P, where P is the price per cup of coffee. For simplicity, we assume Lily's price can not be that high to rule out students' consumption. If StarCoffee cannot distinguish students and professors, what's StarCoffee's optimal price for coffee? (Hint: the aggregated market demand curve has a kink point. So StarCoffee's marginal revenue curve also has a kink point.)